Math is beautiful. Why shouldn’t your notes be? But how much extra time and effort are you willing to spend to ensure it? You see, perfectionism can be both a blessing and a curse. How you manage it determines your success.

Taking good notes begins with the canvas. What do you use for writing notes? Are you getting the most you can get out of it? Alternatively, what don’t you use for writing math notes? Have you ever asked yourself why? Every tool comes with a different set of expectations around the final product, which in turn determines what you do to reach those expectations. It’s important to choose the right tool to guide or constrain yourself into the workflow you desire.

The following list is not meant to be exhaustive. I’ve gone through three different tools over first year, and here are my thoughts on them. Perhaps someday I’ll republish this article with more.

Paper

The old guard, raw and authentic. You’re limited only by the speed of your hand, its endurance, and your paper supply. Oh, the paper supply. Be prepared to take responsibility for the death of a sizeable chunk of a tree over the course of your studies, and to literally bear that weight on your shoulders.

We’ve heard it so many times: nothing beats writing things down by hand. There’s no markup to remember, no shortcuts, no formatting constraints. The lack of that barrier makes it much easier to think about the math you’re doing and not the math you’re writing. This makes paper great for rough work. But for a perfectionist, how do you keep your work rough? How do you limit the amount of effort spent making notes look good, while keeping overall neatness? It’s easy to get lost in your own internal formatting constraints, especially if you use pencil and eraser. Fortunately, some simple anti-perfectionism modifications to your workflow can help.

• Ruin part of the page intentionally. Scribble over a corner in pen, or tear it. If you’re using a notebook, plaster both inside covers with rough work so there’s no hope for having neatness in the pages between.
• Avoid alignment altogether; nothing needs to be centred. Not even your titles. Not even your equations. Not even the date. The consistency of left-aligning everything is enough.
• Adopt a mechanism for inserting corrections that doesn’t involve erasing or crossing out. I use asterisks that point to stuff in the margins.
• The urge to colour-code can be overcome by only carrying one colour of pen. Likewise, the urge to erase can be overcome by not carrying an eraser.

The same raw purity of paper has its downsides. Are you manipulating an annoying series? Be prepared to write each and every sigma — no copy and paste or shortcut for you. Asterisks and erased pencil marks look messy in assignments, so you’ll have to have at least a rough draft for your solution first. And if you ever need it, digitizing your notes is a bit of a pain — it always looks messier once it’s in a screen.

LaTeX

Did someone say shortcuts?

The novelty of picking up a TeX editor for the first time is a true pleasure everyone should experience. It’s also free, so there are almost no excuses. $\LaTeX$ is the tool that automates perfectionism and writes research papers, but there is some overhead.

The most notable barrier to using $\LaTeX$ is the learning curve. Be prepared to spend some time on Stack Exchange, debugging your math. Be prepared for your assignments to take a bit longer to do if you decide to typeset them in $\LaTeX$. It takes a while before you can shoot markup from your fingertips like lightning, but once you can, you’ll feel like a true academic. Anyone who can copy the prof real-time in $\LaTeX$ is a legend. Bonus insanity points if they’re doing it all on the command line.

Writing markup is an added layer of burden when you’re just exploring, so a chalkboard is very helpful in conjunction. There’s nothing that beats perfectionism better than knowing that your work has to be erased. Just be careful about getting dust into your laptop. On the other hand, rendered $\LaTeX$ looks so perfect that anything messed-up sticks out like a sore thumb. You’ll almost certainly be tempted to spend the extra time aligning your equations. You may also be tempted to change the template you’re using, which will add even more time to your work.

The biggest benefit of using $\LaTeX$ (other than pure perfection) is code reuse. The simpler form of this is copy-paste. If you’re doing some high school algebra, duplicating an equation and editing the copy can often be easier than typing out a whole new one. The more advanced form is defining your own shortcuts. This is an absolute must if you’re using $\LaTeX$ for calculus.

Microsoft Word and Google Docs

Expect a bit of ridicule for this one, but it works. Just like how you can mess up your notebook to perfection-proof your physical notes, using either of these is a great way to perfection-proof your digital notes.

They’re both awful. Specifically, their equation editors are awful. Even if they have built-in $\LaTeX$, the interface feels wrong and the experience is ruined. There’s no chance for you to make them look good, so there’s not much of a point in trying. Use this for whipping up a super-fast assignment solution, or if you’re typing what your prof is saying but can’t yet shoot $\LaTeX$ out of your fingertips.

The added benefit of a word processor is that it’s WYSIWYG: What You See Is What You Get, no extra thinking about how to manage your markup. (But then again, you can also get $\LaTeX$ to do that too… just with a lot of work.)